A new method of calculation of Franck–Condon factors which includes allowance for anharmonicity and the Duschinsky effect: Simulation of the He I photoelectron spectrum of ClO2

Abstract

A new method of Franck-Condon ͑FC͒ factor calculation for nonlinear polyatomics, which includes anharmonicity and Duschinsky rotation, is reported. Watson's Hamiltonian is employed in this method with multidimensional ab initio potential energy functions. The anharmonic vibrational wave functions are expressed as linear combinations of the products of harmonic oscillator functions. The Duschinsky effect, which arises from the rotation of the normal modes of the two electronic states involved in the electronic transition, is formulated in Cartesian coordinates, as was done previously in an earlier harmonic FC model. This new anharmonic FC method was applied to the simulation of the bands in the He I photoelectron ͑PE͒ spectrum of ClO 2 . For the first band, the harmonic FC model was shown to be inadequate but the anharmonic FC simulation gave a much-improved agreement with the observed spectrum. The experimentally derived geometry of the X 1 A 1 state of ClO 2 ϩ was obtained, for the first time, via the iterative FC analysis procedure ͕R(Cl-O͒ϭ1.414Ϯ0.002 Å, ЄO-Cl-Oϭ121.8Ϯ0.1°͖. The heavily overlapped second PE band of ClO 2 , corresponding to ionization to five cationic states, was simulated using the anharmonic FC code. The main vibrational features observed in the experimental spectrum were adequately accounted for in the simulated spectrum. The spectral simulation reported here supports one of the two sets of published assignments for this band, which was based on multireference configuration interaction ͑MRCI͒ calculations. In addition, with the aid of the simulated envelopes, a set of adiabatic ͑and vertical͒ ionization energies to all five cationic states involved in this PE band, more reliable than previously reported, has been derived. This led also to a reanalysis of the photoabsorption spectrum of ClO 2 .

Anharmonic Franck–Condon Factors for the X̃2B1 ← X̃1A1 Photoionization of Ketene

“…33 It shall be noted here that Duschinsky effects have also been accounted for by other authors within the determination of Franck-Condon factors in many anharmonic calculations for triatomic systems, but also for more extended systems. 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 which led to a sum of FCFs being larger than 0.9999. From these the most important have been selected, which were subsequently computed by state-specific configuration-selective VCI calculations with configuration spaces including quadruple excitations and accounting for vibrational angular momentum terms.…”

The geometry of the NO2− anion: ab initio calculations and Franck–Condon analysis

“…Botschwina et al [15] are one of the few research groups performing anharmonic FCF calculations in this way. Recently, details of a few other types of anharmonic FCF methods have been published [12][13][14][16][17][18]. Franck-Condon factor calculations that consider anharmonicity effects will be the focus of our future work.…”

“…Geometry optimization and harmonic vibrational frequency calculations were carried out on theX 2 [8,[10][11][12][13][14] was also carried out.…”

Ab initio calculations and Franck–Condon analysis of photoelectron spectroscopy of CH3OO− and CD3OO−

“…With quantum chemical computing programs being readily available, geometries and normal modes of small to medium size molecules in different electronic states can now be calculated routinely. Based on these methods, numerous applications of FC calculations have been presented in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14], and most of these studies just focus on the interpretation of experimentally known spectra. Because the geometry difference between two electronic states is a major factor that influences FC intensities, the simulation of vibronic spectra of ployatomic molecules can be regarded as a valuable test with respect to the quality of calculated geometries and as a starting point to obtain improved structures.…”

“…In addition, spectral simulations of vibrational structure based on computed Franck-Condon factors (FCF) could provide fingerprint type identification of an observed spectrum, in terms of both the carrier and the electronic states in the transition (see, for examples, [9,10], and references therein). Also, it has been demonstrated that spectral simulations can be very useful in establishing vibrational assignments in an electronic spectrum observed with complex vibrational structure [1][2][3][4][5]7,10,11].…”